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A065775 Array T read by diagonals: T(i,j)=least number of knight's moves on a chessboard (infinite in all directions) needed to move from (0,0) to (i,j). 17
0, 3, 3, 2, 2, 2, 3, 1, 1, 3, 2, 2, 4, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 2, 2, 2, 4, 4, 5, 3, 3, 3, 3, 3, 3, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 3, 3, 3, 3, 5, 5, 5, 6, 6, 4, 4, 4, 4, 4, 4, 4, 6, 6, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 6, 6, 6, 6, 4, 4, 4, 4, 4, 6, 6, 6, 6, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 7 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
For number of knight's moves to various subsets of the chessboard, see A018837, A183041 - A183053.
LINKS
FORMULA
T(i,j) is given in cases:
Case 1: row 0
T(0,0)=0, T(1,0)=3, and for m>=1,
T(4m-2,0)=2m, T(4m-1,0)=2m+1, T(4m,0)=2m,
T(4m+1,0)=2m+1.
Case 2: row 1
T(0,1)=3, T(1,1)=2, and for m>=2,
T(4m-2,1)=2m-1, T(4m-1,1)=2m, T(4m,1)=2m+1,
T(4m+1,1)=2m+2.
Case 3: columns 1 and 2
(column 1) = (row 1); (column 2 = row 2).
Case 4: For i>=2 and j>=2,
T(i,j)=1+min{T(i-2,j-1),T(i-1,j-2)}.
Cases 1-4 determine T in the 1st quadrant;
all other T(i,j) are easily obtained by symmetry.
EXAMPLE
T(i,j) for -2<=i<=2 and -2<=j<=2:
4 1 2 1 4=T(2,2)
1 2 3 2 1=T(2,1)
2 3 0 3 2=T(2,0)
1 2 3 2 1=T(2,-1)
4 1 2 1 4=T(2,-2)
Corner of the array, T(i,j) for i>=0, k>=0:
0 3 2 3 2 3 4...
3 2 1 2 3 4 3...
2 1 4 3 2 3 4...
3 2 3 2 3 4 2...
CROSSREFS
Identical to A049604 except for T(1, 1).
Cf. A183041,...,A183042.
Sequence in context: A064983 A124933 A133884 * A096837 A139092 A366424
KEYWORD
nonn,tabl
AUTHOR
Stewart Gordon, Dec 05 2001
EXTENSIONS
Formula, examples, and comments by Clark Kimberling, Dec 20 2010
Example corrected by Clark Kimberling, Oct 14 2016
STATUS
approved

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Last modified April 15 20:47 EDT 2024. Contains 371696 sequences. (Running on oeis4.)